I have always thought that there are three possible answers to the question what is 0 / 0:

zero, since zero divided by anything is still zero;

infinity, since anything divided by zero is infinity;

one, since anything divided by itself is one.

Of course my thinking can be very wrong as zero is not just anything -- it is a special case in itself. 0 / 0 may be equal to zero, one and infinity at the same time, but it is probably easier to say that it is undefined. Or even Mu.

Yes, the answer is that the result of x/0 (including x=0) is every possible result at once. That is because x*0 is zero for any x. With x*a for any a != 0 the result set is exactly as large as the definition set (I hope these are the correct English terms). But for a = 0, the result set has only a single value, 0 itself.

x*a maps every x to one distinct y, except for a=0, so you can reverse it. But for a=0, it maps every x to the same y (that is, to 0), so by knowing a=0 and y=0 you still cannot tell which out of an infinite number of possible values for x led to this result.

Ada Lovelace for the palindrome
Albert Einstein for having smelly feet
Alfred Nobel for his contribution to battlefield science
Burkhard Heim for providing the missing link between science and mysticism
Claude Shannnon for riding a unicycle at night at MIT
Donald Knuth for being such a great organist
Edward Teller for being the template for Dr. Strangelove
Edwin Hubble for pretending to be a pipe-smoking English gentleman
Erwin Schrödinger for cruelty to cats
Hedy Lamarr for weaponizing pianos
Hugh Everett for immortality, especially for cats
Isaac Newton for his occult studies
Kikunae Ikeda for discovering the secrets of soy sauce
Larry Wall for his website
Louis Camille Maillard for discovering why steaks taste good
Marie Curie for the shiny stuff
Nikola Tesla for the cool cars
Paul Dirac for speaking one word per hour when socializing
Richard Feynman for his bongo skills
Robert Oppenheimer for his in-depth knowledge of the Bhagavad Gita
Rusi P Taleyarkhan for Cold Fusion
Sigmund Freud for his Ménage ā trois
Theodor W Adorno for his contribution to the reception of jazz
Wilhelm Röntgen for the foundations of body scanners
Yulii Borisovich Khariton for the Tsar Bomba
Other (please explain why)